Electron. J. Diff. Equ., Vol. 2012 (2012), No. 58, pp. 1-9.

Existence of bounded positive solutions of a nonlinear differential system

Sabrine Gontara

In this article, we study the existence and nonexistence of solutions for the system
 \frac{1}{A}(Au')'=pu^{\alpha }v^{s}\quad \hbox{on }(0,\infty ), \cr
 \frac{1}{B}(Bu')'=qu^{r}v^{\beta }\quad \hbox{on }(0,\infty ), \cr
 Au'(0)=0,\quad u(\infty )=a>0, \cr
 Bv'(0)=0,\quad v(\infty )=b>0,
where $\alpha ,\beta \geq 1$, $s,r\geq 0$, p,q are two nonnegative functions on $(0,\infty )$ and A, B satisfy appropriate conditions. Using potential theory tools, we show the existence of a positive continuous solution. This allows us to prove the existence of entire positive radial solutions for some elliptic systems.

Submitted January 20, 2012. Published April 10, 2012.
Math Subject Classifications: 35J56, 31B10, 34B16, 34B27.
Key Words: Nonlinear equation; Green's function; asymptotic behavior; singular operator; positive solution.

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Sabrine Gontara
Dépatement de mathématiques
Faculté des sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: sabrine-28@hotmail.fr

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